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Simplifying 2y2 + -8y = 540 Reorder the terms: -8y + 2y2 = 540 Solving -8y + 2y2 = 540 Solving for variable 'y'. Reorder the terms: -540 + -8y + 2y2 = 540 + -540 Combine like terms: 540 + -540 = 0 -540 + -8y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-270 + -4y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-270 + -4y + y2)' equal to zero and attempt to solve: Simplifying -270 + -4y + y2 = 0 Solving -270 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + -4y + 270 + y2 = 0 + 270 Reorder the terms: -270 + 270 + -4y + y2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -4y + y2 = 0 + 270 -4y + y2 = 0 + 270 Combine like terms: 0 + 270 = 270 -4y + y2 = 270 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 270 + 4 Reorder the terms: 4 + -4y + y2 = 270 + 4 Combine like terms: 270 + 4 = 274 4 + -4y + y2 = 274 Factor a perfect square on the left side: (y + -2)(y + -2) = 274 Calculate the square root of the right side: 16.552945357 Break this problem into two subproblems by setting (y + -2) equal to 16.552945357 and -16.552945357.Subproblem 1
y + -2 = 16.552945357 Simplifying y + -2 = 16.552945357 Reorder the terms: -2 + y = 16.552945357 Solving -2 + y = 16.552945357 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 16.552945357 + 2 Combine like terms: -2 + 2 = 0 0 + y = 16.552945357 + 2 y = 16.552945357 + 2 Combine like terms: 16.552945357 + 2 = 18.552945357 y = 18.552945357 Simplifying y = 18.552945357Subproblem 2
y + -2 = -16.552945357 Simplifying y + -2 = -16.552945357 Reorder the terms: -2 + y = -16.552945357 Solving -2 + y = -16.552945357 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -16.552945357 + 2 Combine like terms: -2 + 2 = 0 0 + y = -16.552945357 + 2 y = -16.552945357 + 2 Combine like terms: -16.552945357 + 2 = -14.552945357 y = -14.552945357 Simplifying y = -14.552945357Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.552945357, -14.552945357}Solution
y = {18.552945357, -14.552945357}
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